David Layzer is a Harvard cosmologist who in the 1960's made it clear that in an expanding universe entropy would increase, as required by the second law of thermodynamics, but that the maximum possible entropy of the universe might increase faster than the actual entropy increase, making room for the growth of order or information at the same time entropy is increasing.

He pointed out that if the equilibration rate of the matter was slower than the rate of expansion, then the "negative entropy" (defined as the difference between the maximum possible entropy and the actual entropy) would increase. Claude Shannon identified this negative entropy with information, though visible structural information in the universe may be less than this "potential" information.

If everything that happens was certain to happen, as determinist philosophers claim, no new information would ever enter the universe. Information would be a universal constant. There would be "nothing new under the sun." Every past and future event can in principle be known (as Pierre-Simon Laplace suggested) by a super-intelligence with access to such a fixed totality of information.

It is of the deepest philosophical significance that information is based on the mathematics of probability. If all outcomes were certain, there would be no “surprises” in the universe. Information would be conserved and a universal constant, as some mathematicians mistakenly believe. Information philosophy requires the ontological uncertainty and probabilistic outcomes of modern quantum physics to produce new information.

From Newton’s time to the start of the 19th century, the Laplacian view coincided with the notion of the divine foreknowledge of an omniscient God. On this view, complete, perfect and constant information exists at all times that describes the designed evolution of the universe and of the creatures inhabiting the world.

In this God’s-eye view, information is a constant of nature. Some mathematicians argue that information must be a conserved quantity, like matter and energy. They are wrong. In Laplace's view, information would be a constant straight line over all time, as shown in the figure.

If information were a universal constant, there would be “nothing new under the sun.” Every past and future event can in principle be known by Laplace's super-intelligent demon , with its access to such a fixed totality of information.

Since William Thomson (Lord Kelvin), James Clerk Maxwell, and Ludwig Boltzmann, most physicists and astronomers have believed that the universe began with a high degree of organization or order (or information) and that it has been running down ever since.
Hermann Helmholtz described this as the “heat death” of the universe.

Mathematicians who are convinced that information is always conserved argue that macroscopic order is disappearing into microscopic order, but the information could in principle be recovered, if time could only be reversed.

This raises the possibility of some connection between the increasing entropy and what Arthur Stanley Eddington called “Time’s Arrow.”

Kelvin’s claim that information must be destroyed when entropy increases would be correct if the universe were a closed system. But in our open and expanding universe, Layzer showed that the maximum possible entropy is increasing faster than the actual entropy. The difference between maximum possible entropy and the current entropy is called negative entropy, opening the possibility for complex and stable information structures to develop.

We can see from the figure that it is not only entropy that increases in the direction of the arrow of time, but also the information content of the universe. We can describe the new information as "emerging."

Layzer showed that this standard view was wrong for our expanding universe.

Roger Penrose

In his 1989 book The Emperor's New Mind, Penrose speculated on the connection between information, entropy, and the arrow of time.

Recall that the primordial fireball was a thermal state — a hot gas in expanding thermal equilibrium. Recall, also, that the term 'thermal equilibrium' refers to a state of maximum entropy. (This was how we referred to the maximum entropy state of a gas in a box.) However, the second law demands that in its initial state, the entropy of our universe was at some sort of minimum, not a maximum!

What has gone wrong? One 'standard' answer would run roughly as follows:

True, the fireball was effectively in thermal equilibrium at the beginning, but the universe at that time was very tiny. The fireball represented the state of maximum entropy that could be permitted for a universe of that tiny size, but the entropy so permitted would have been minute by comparison with that which is allowed for a universe of the size that we find it to be today. As the universe expanded, the permitted maximum entropy increased with the universe's size, but the actual entropy in the universe lagged well behind this permitted maximum. The second law arises because the actual entropy is always striving to catch up with this permitted maximum.

(The Emperor's New Mind, p.328-9)

Clearly, Penrose's "standard" answer is the work of David Layzer. Penrose met Layzer at a 1973 conference at Cornell University on the "Arrow of Time."

The Arrow of Time

Layzer identified what he called the "historical arrow of time" (the direction of increasing information) with the "thermodynamic arrow of time." The phrase "time's arrow" was coined by Arthur Stanley Eddington.

Isolated systems inevitably evolve
toward the featureless state of thermodynamic
equilibrium. Since the universe
is in some sense an isolated system, why
has it not settled into equilibrium? One
answer, favored by many cosmologists,
is that the cosmological trend is in fact
toward equilibrium but that too little
time has elapsed for the process to have
reached completion. Fred Hoyle and
J. V. Narlikar have written: "In the 'big
bang' cosmology the universe must start
with a marked degree of thermodynamic
disequilibrium and must eventually run
down." I shall argue that this view is
fundamentally incorrect. The universe is
not running down, and it need not have
started with a marked degree of disequilibrium;
the initial state may indeed
have been wholly lacking in macroscopic
as well as microscopic information.

Suppose that at some early moment
local thermodynamic equilibrium prevailed
in the universe. The entropy of
any region would then be as large as
possible for the prevailing values of the
mean temperature and density. As the
universe expanded from that hypothetical
state the local values of the mean
density and temperature would change,
and so would the entropy of the region.
For the entropy to remain at its maximum
value (and thus for equilibrium to
be maintained) the distribution of energies
allotted to matter and to radiation
must change, and so must the concentrations
of the various kinds of particles.
The physical processes that mediate
these changes proceed at finite rates;
if these "equilibration" rates are all much
greater than the rate of cosmic expansion,
approximate local thermodynamic
equilibrium will be maintained; if they
are not, the expansion will give rise to
significant local departures from equilibrium.

These departures represent
macroscopic information; the quantity of
macroscopic information generated by
the expansion is the difference between
the actual value of the entropy and
the theoretical maximum entropy at the
mean temperature and density.

(Scientific American, December, 1975, p.68)

Layzer specifically identified this process as generating novelty and contradicting a deterministic view of the world, with significant implications for human freedom:

Novelty and Determinism

We have now traced the thermodynamic
arrow and the historical arrow to
their common source: the initial state of
the universe. In that state microscopic
information is absent and macroscopic
information is either absent or minimal.
The expansion from that state has generated
entropy as well as macroscopic
structure. Microscopic information, on
the other hand, is absent from newly
formed astronomical systems, and that is
why they and their subsystems exhibit
the thermodynamic arrow.

This view of the world evolving in
time differs radically from the one that
has dominated physics and astronomy
since the time of Newton, a view that
finds its classic expression in the words of
Pierre Simon de Laplace: "An intelligence
that, at a given instant, was acquainted
with all the forces by which nature
is animated and with the state of the
bodies of which it is composed, would - if
it were vast enough to submit these
data to analysis - embrace in the same
formula the movements of the largest
bodies in the Universe and those of the
lightest atoms: nothing would be uncertain
for such an intelligence, and the future
like the past would be present to its
eyes."

In Laplace's world there is nothing
that corresponds to the passage of time.
For Laplace's "intelligence," as for the
God of Plato, Galileo and Einstein, the
past and the future coexist on equal
terms, like the two rays into which an
arbitrarily chosen point divides a straight
line. If the theories I have presented
here are correct, however, not even the
ultimate computer - the universe itself - ever
contains enough information to
completely specify its own future states.
The present moment always contains an
element of genuine novelty and the future
is never wholly predictable. Because
biological processes also generate
information and because consciousness
enables us to experience those processes
directly, the intuitive perception of the
world as unfolding in time captures one
of the most deep-seated properties of the
universe.

(Scientific American, December, 1975, p.69)

Note that the deterministic Laplacian universe contains exactly the same information at all times - nothing new under the sun.

In 1990, Layzer extended these ideas in his book Cosmogenesis: The Growth of Order in the Universe. He added a discussion of quantum mechanics and its implications for free will. First he noted a number of paradoxes, between microscopic quantum systems and the macroscopic universe, between standard thermodynamic macrophysics and cosmology, between irreducible randomness and human ignorance, and between the objective timeless being of the Laplacian view and the subjective human experience of becoming and change.

Conflicts and Paradoxes

The relation between quantum physics, which describes the invisible world of elementary particles and their interactions, and macroscopic physics, which describes the world of ordinary experience, has perplexed physicists since the birth of quantum physics in 1925. Viewed as a system of mathematical laws, quantum physics includes macroscopic physics as a limiting case. By that I mean that quantum physics and macroscopic physics make the same predictions in the domain where macroscopic physics has been strongly corroborated (the macroscopic domain), but quantum physics also successfully describes the behavior and structure of molecules; atoms, and subatomic particles (the microscopic domain). Yet from another point of view, macroscopic physics seems more fundamental than quantum physics. As we will see later, the laws of quantum physics refer explicitly to the results of measurement. But every measurement necessarily has at least one foot in the world of ordinary experience: it has to be recorded in somebody's lab notebook or on magnetic tape. So quantum physics seems to presuppose its own limiting case — macroscopic physics. This is the mildest of several paradoxes that have sprung up in the region where quantum physics and macrophysics meet and overlap.

The relation between macrophysics and cosmology is also problematic. The central law of macroscopic physics — the second law of thermodynamics — was understood by its inventors, and is still understood by most scientists, to imply that the Universe is running down — that order is degenerating into chaos. How can we reconcile such a tendency with the fact that the world is full of order — that it is a kosmos in both senses of the word. Some scientists say, "The contradiction is only apparent, The Second Law assures us that the Universe is running down, so it must have begun with a vast supply of order that is gradually being
dissipated. But this way of trying to resolve the difficulty takes us from the frying pan into the fire, because, as we will see, modern cosmology strongly suggests that the early Universe contained far less order than the present-day Universe.

Astronomical evolution and biological evolution are both stories of emerging order. Nevertheless, the views of time and change implicit in modern physics and modern biology are radically different. The physical sciences teach us that all natural phenomena are governed by mathematical laws that connect every physical event with earlier and later events. Imagine that every past and future event was recorded on an immense roll of film. If we knew all the physical laws, we could reconstruct the whole film from a single frame. And in principle there is nothing to prevent us from acquiring complete knowledge of a single frame.

This worldview is epitomized in a much-quoted passage by one of Newton's most illustrious successors, the mathematician and theoretical astronomer Pierre Simon de Laplace (1749-1827):

We ought then to regard the present state of the Universe as the effect of its previous state and the cause of the one that follows. An intelligence that at a given instant was acquainted with all the forces by which nature is animated and with the state of the bodies of which it is composed would — if it were vast enough to submit these data to analysis — embrace in the same formula the movements of the largest bodies in the Universe and those of the lightest atoms: Nothing would be uncertain for such an intelligence, and the future like the past would be present to its eyes. The human mind offers, in the perfection it has been able to give to astronomy, a feeble idea of this intelligence.

The scientist is possessed by the sense of universal causation. The future, to him, is every whit as necessary and determined as the past.

Most contemporary physical scientists would probably agree with Laplace and Einstein. The world they study is a block universe, a four-dimensional net of causally connected events with time as the fourth dimension. In this world, no moment in time is singled out as "now." For Laplace's Intelligence, the future and the past don't exist in an absolute sense, as they do for us.

How does life, regarded as a scientific phenomenon, fit into this worldview? A modern Laplacian might reply:
Living organisms are collections of molecules that move and interact with one another and with their environment according to the same laws that govern molecules in nonliving matter. A supercomputer, supplied with a complete microscopic description of the biosphere and its environment, would be able to predict the future of life on Earth and to deduce its initial state. Implicit in the present state of the biosphere and its environment are the precise conditions that prevailed in the lifeless broth of organic molecules in which the first self-replicating molecules formed, And implicit in the conditions that prevailed in that broth and its environment is every detail of the living world of today. If you believe that living matter is subject to the same laws as nonliving matter and few, if any, contemporary biologists would dispute this assertion - this argument may seem compelling. Yet it clashes with two key aspects of the evolutionary process as described by contemporary evolutionary biologists: randomness and creativity.

Randomness is an essential feature of the reproductive process. In nearly every biological population, new genes and new combinations of genes appear in every generation. Reproduction, whether sexual or asexual, involves the copying of genetic material (DNA). In all modern organisms the copying process is astonishingly accurate. But it isn't perfect. Occasionally there are copying errors, and these have a random character. In sexually reproducing populations there is another source of randomness: the genetic material of each individual is a random combination of contributions from each parent.

The creative factor in biological evolution is natural selection, the tendency of genetic changes that favor survival and reproduction to spread in a population, and of changes that hinder survival and reproduction to die out. From the raw material provided by genetic variation, natural selection fashions new biological structures, functions, and behaviors.

A mainstream physicist might reply that the apparent randomness of genetic variation is just a consequence of human ignorance — our inability to understand exceedingly complex but nevertheless completely determinate causal processes — and that evolution is "creative" only in a metaphorical sense. According to this view, evolution merely brings to light varieties of order prefigured in the prebiotic broth.

There is an even more fundamental difference between the physical and the biological views of reality: the physicist's picture of reality seems impossible to reconcile with subjective experience. For there is nothing in the neo-Laplacian picture that corresponds to the central feature of human experience, the passage of time. We humans must watch the film unwind, but Laplace's Intelligence sees it whole. Nor is there anything that corresponds to the aspect of reality (as we experience it) that Greek philosophers called becoming, as opposed to the timeless being of numbers, triangles, and circles. The universe of modern physics is an enormously expanded and elaborated version of the perfectly ordered but static and lifeless world we encounter in Euclid's Elements, of which it is indeed a direct descendant. The biologist's world seems entirely different. Life, as we experience it, is inseparable from unpredictability and novelty.

(Cosmogenesis, pp.5-6)

Layzer then examines the role of chance in human freedom and finds that no one has been able to explain what even fundamental quantum mechanical randomness has to do with free choice and moral responsibility.

Freedom and Necessity

What is the relation between being and becoming? Is the future as fixed and immutable as the past? What is chance? These questions bear on one of the perennial problems of Western philosophy, the problem of freedom and necessity.

Each of us belongs to two distinct worlds. As objects in the world that natural science describes we are governed by universal laws. To Laplace's Intelligence we are systems of molecules whose movements are no less predicable and no more the results of free choice than the movements of the planets around the Sun. but as the subjects of our own experience we see the world differently; not as bundles of events frozen into the block universe of Laplace and Einstein like flies in amber, but as the authors of our own actions, the molders of our own lives. However strongly we may believe in the universality of physical laws, we cannot suppress the intuitive conviction that the future is to some degree open and that we help to shape it by our own free choices.

This conviction lies at the basis of every ethical system. Without freedom there can be no responsibility. If we are not really free agents — if our felt freedom is illusory — how can we be guided in our behavior by ethical precepts? And why should society punish some acts and reward others? The Laplacian worldview tends to undermine the basis for ethical behavior.

Judeo-Christian theology faces a similar problem. Although Laplace's Intelligence is not the Judeo-Christian God — Laplace's Intelligence observes and calculates; the Judeo-Christian God wills and acts ("Necessitie and chance approach not mee, and what I will is Fate," says the Almighty in Milton's Paradise Lost)— they contemplate similar universes. Nothing is uncertain for an all-knowing God, and the future, like the past, is present to His eyes. But if we cannot choose where we walk, why should those who take the narrow way of righteousness be rewarded in the next life while those who take the primrose path are consigned to the flames of hell?

Theologians have not, of course, neglected this question. Augustine, for example, argued that God's foreknowledge (or more accurately, God's knowledge of what we call the future) doesn't cause events to happen and is therefore consistent with human free will. Other theologians have embraced the doctrine of predestination and argued that free will is indeed an illusion. Still others have taken the position that divine omniscience and human free will are compatible in a way that surpasses human understanding.

Reconciling the scientific and ethical pictures of the world was a concern of the first scientists. Our scientific picture of the world was foreshadowed by Greek atomism, a theory invented by the natural philosophers Leucippus and Democritus in the fifth century B.C. According to this theory, the world is made up of unchanging, indestructible particles moving about in empty space and interacting with one another in a completely deterministic way. Like modern biologists, Democritus believed that we, too, are assemblies of atoms. Yet Democritus also elaborated a system of ethics based on moral responsibility. He taught that we should do what is right not from fear, whether of punishment or of public disapproval or of the wrath of gods, but in response to our own sense of right and wrong. Unfortunately, the surviving fragments of Democritus's writings don't tell us how or whether he was able to reconcile his deterministic picture of nature with his doctrine of moral responsibility.

A century later, another Greek philosopher with similar ideas about physical reality and moral responsibility faced the same dilemma. Epicurus (341-270 B.C.) sought to reconcile human freedom with the atomic theory by postulating a random element in atomic interactions. Atoms, he said, occasionally "swerve" unpredictably from their paths. In modern times, Arthur Stanley Eddington and other scientists have put forward more sophisticated versions of the same idea. According to quantum physics, it is impossible to predict the exact moment when certain atornic events, such as the decay of a radioactive nucleus, will take place. Eddington believed that this kind of microscopic indeterminism might provide a scientific basis for human freedom:

It is a consequence of the advent of quantum theory that physics is no longer pledged to a scheme of deterministic laws. . . . The future is a combination of the causal influences of the past together with unpredictable elements. . [S]cience thereby withdraws its moral opposition to free will.

But neither Epicurus nor Eddington explained what the "freedom" enjoyed by a swerving atom or a radioactive atomic nucleus has to do with the freedom of a human being to choose between two courses of action. Nor has anyone else.

(Cosmogenesis, pp.6-7)

Layzer reaffirms his 1975 claim about the initial state of the universe lacking significant order or information, but he does not tell us that a theory of the growth of order goes back to the 1960's and is his original contribution.

We need not assume, as Clausius and Boltzmann did in the nineteenth century and - as many modern astronomers and physicists still do, that the Universe started out with a huge store of order that it has been gradually dissipating ever since. If the hypothesis outlined in this chapter is correct, the initial state of the Universe was wholly lacking in order.
(Cosmogenesis, p.170)

In the concluding chapter of Cosmogenesis, Layzer revisits the problem of human freedom and especially creativity. Although he offers no resolution of the free will problem, he places great emphasis on an unpredictable creativity as the basis of both biological evolution and human activity in a universe with an open future.

Chapter 15: Chance, Necessity, and Freedom

To be fully human is to be able to make deliberate choices. Other animals sometimes have, or seem to have, conflicting desires, but we alone are able to reflect on the possible consequences of different actions and to choose among them in the light of broader goals and values. Because we have this capacity we can be held responsible for our actions; we can deserve praise and blame, reward and punishment. Values, ethical systems, and legal codes all presuppose freedom of the will. So too, as P. F. Strawson has pointed out, do "reactive attitudes" like guilt, resentment, and gratitude. If I am soaked by a summer shower I may be annoyed by my lack of foresight in not bringing an umbrella, but I don't resent the shower. I could have brought the umbrella; the shower just happened.

Freedom has both positive and negative aspects. The negative aspects — varieties of freedom from — are the most obvious. Under this heading come freedom from external and internal constraints. The internal constraints include ungovernable passions, addictions, and uncritical ideological commitments.
The positive aspects of freedom are more subtle. Let's consider some examples.

1. A decision is free to the extent that it results from deliberation. Absence of coercion isn't enough. Someone who bases an important decision on the toss of a coin seems to be acting less freely than someone who tries to assess its consequences and to evaluate them in light of larger goals, values, and ethical precepts.

2. Goals, values, and ethical precepts may themselves be accepted uncritically or under duress, or we may feel free to modify them by reflection and deliberation. Many people don't desire this kind of freedom and many societies condemn and seek to suppress it. Freedom and stability are not easy to reconcile, and people who set a high value on stability tend to set a correspondingly low value on freedom. But whether or not we approve of it, the capacity to reassess and reconstruct our own value systems represents an important aspect of freedom.

3. Henri Bergson believed that freedom in its purest form manifests itself in creative acts, such as acts of artistic creation. Jonathan Glover has argued in a similar vein that human freedom is inextricably bound up with the "project of self-creation." The outcomes of creative acts are unpredictable, but not in the
same way that random outcomes are unpredictable. A lover of Mozart will immediately recognize the authorship of a Mozart divertimento that he happens not to have heard before. The piece will "sound like Mozart." At the same time, it will seem new and fresh; it will be full of surprises. If it wasn't, it wouldn't be Mozart. In the same way, the outcomes of self-creation are new and unforeseeable, yet coherent with what has gone before.

Although philosophical accounts of human freedom differ, they differ surprisingly little. On the whole, they complement rather than conflict with one another. What makes freedom a philosophical problem is the difficulty of reconciling a widely shared intuitive conviction that human beings are or can be free (in the ways discussed above or in similar ways) with an objective view of the world as a causally connected system of events. We feel ourselves to be free and responsible agents, but science tells us (or seems to tell us) that we are collections of molecules moving and interacting according to strict causal laws.

For Plato and Aristotle, there was no real difficulty. They believed that the soul initiates motion — that acts of will are the first links of the causal chains in which they figure. With few exceptions, modern neurobiologists have rejected the view of the relation between mind and body that this doctrine implies. They regard mental processes as belonging to the natural world, subject to the same physical laws that govern inanimate matter. The differences between animate and inanimate systems and between conscious, and nonconscious nervous processes are not caused by the presence or absence of nonmaterial substances (the breath of, life, mind, spirit, soul) but by the presence or absence of certain kinds of order. This conclusion is more than a profession of scientific faith. It becomes unavoidable once we accept the hypothesis of biological evolution, without which, as Theodosius Dobzhansky remarked, nothing in biology makes sense. The evolutionary hypothesis implies that human consciousness evolved from simpler kinds of consciousness, which in turn evolved from nonconscious forms of nervous activity. There is no point in this evolutionary sequence where mind or spirit or soul can plausibly be assumed to have inserted itself "from without." It seems even more implausible to suppose that it was there all along, although, as we saw earlier, some modem philosophers and scientists have held this view.

Karl Popper and other philosophers have tried to resolve the apparent conflict between free will and determinism by attacking the most sacred of natural science's sacred cows, the assumption that all natural processes obey physical laws.

In asserting that there may be phenomena that don't obey physical laws, these philosophers are obviously on safe ground. But the assumption of indeterminism doesn't really help. A freely taken decision or a creative act doesn't just come into being. It is the necessary — and hence law-abiding — outcome of a complex process. Free actions also have predictable — and hence lawful - consequences; otherwise, planning and foresight would be futile. Thus every free act belongs to a causal chain: it is the necessary outcome of a deliberative or creative process, and it has predictable consequences.

Some physicists and philosophers have suggested that quantal indeterminacy may provide leeway for free acts in an otherwise deterministic Universe. Freedom, however, doesn't reside in randomness; it resides in choice. Plato and Aristotle were right in linking Chance and Necessity as "forces" opposed to design and purpose in the Universe.

Thus freedom seems equally inconsistent with determinism and indeterminism. Thomas Nagel has suggested that it isn't even possible to give a coherent account of our inner sense of freedom:

When we try to explain what we believe which seems to be undermined by a conception of actions as events in the world - determined or not — we end up with something that is either incomprehensible or clearly inadequate.

"The real problem," Nagel says, "stems from a clash between the view of action from inside and any view of it from outside." Yet the intuitive view of what it means to be free doesn't rest on introspection alone. We recognize other people's spontaneity and creativity even — or especially — when it is of such a high order that we can't imagine ourselves capable of it. We can apprehend the exquisitely ordered unpredictability of Mozart's music without beginning to be able to imagine what it would be like to compose such music. And even subjective impressions of freedom, unlike subjective impressions of pain or of self, aren't hard to describe.

Consider the process of making a decision. Shall I do A or B? My head says A; my heart says B. I agonize. I try to imagine the consequences first of A, then of B. Suddenly, a new thought occurs to me: C. Yes, I'll do C. The essential aspect of such commonplace experiences is that their outcomes aren't determined in advance but are created by the process of deliberation itself, a process unfolding in time. All creative processes have this character.

Such processes, however, go on not only in people's subjective awareness but also in their brains. Conscious experience gives us a fragmentary and unrepresentative view of its underlying cerebral processes, but there is no reason to suppose that the view is deceptive. On the contrary, modern techniques of imaging brain activity suggest that there is a high degree of structural correspondence between consciousness and brain activity.

If, then, the outcome of a deliberative or creative process seems undetermined at the outset, if it seems to us that such processes create their outcomes, perhaps the reason is that the outcomes of the underlying cerebral processes are, in some objective sense, undetermined, are, in some objective sense, created by the processes themselves.

I will argue that the neural processes that give rise to subjective experiences of freedom are indeed creative processes, in the sense, that they bring into the world kinds of order that didn't exist earlier and weren't prefigured in earlier physical states. These novel and unforeseen products of neural activity include not only works of art, but also the evolving patterns of synaptic connections that underlie the intentions, plans, and projects that guide our commonplace activities. Although consciousness gives us only superficial and incomplete glimpses of this ceaseless constructive activity, we are aware of it almost continuously during our waking hours. This awareness may be the source of — or even constitute — the subjective impression that we participate in molding the future.

Much of the argument that supports this view has already been given in earlier chapters. Let me now try to pull it together around the following three questions:

1. Do all law-abiding processes have predetermined outcomes?
2. What does it mean to say that a physical process creates its outcomes?
3. How is this kind of creativity related to creativity in contexts relevant to the problem of human freedom?

[Answer to question 1]: Do all law-abiding processes have predetermined outcomes? Outcomes are determined by laws plus initial conditions. They are undetermined to the extent that the initial conditions are unspecified.

[Answer to question 2]: A theory of cosmic evolution requires initial conditions. The simplest initial
conditions is that the Universe began to expand from a purely random state — a
state wholly devoid of order. From this postulate, we can easily deduce the Strong
Cosmological Principle. The inference hinges on the fact that none of our present
physical laws discriminates between different points in space or between different
directions at a point. (A physicist would say, "The laws are invariant under spatial translations and rotations.") This implies that no physical process can introduce discriminatory information. So if information that would discriminate between positions or directions is absent at a single moment, it must be absent forever. In short, if the Strong Cosmological Principle is valid at any single moment, it must be valid for all time.

If the Universe began to expand from a state of utter randomness, how did order come into being? Before reviewing our answer to this question, we have to recall how we dealt with the concept of order itself.

The two key ideas needed to formulate an adequate scientific definition of order were put forward by Ludwig Boltzmann.

The first idea is the distinction between microstates and macrostates. Macrostates are groups of microstates, defined by their statistical properties. For example, the microstates of a gas may be assigned to macrostates defined by density, temperature, and chemical composition. Proteins may be assigned to macrostates defined by biological fitness. Boltzmann's second key idea was to identify the randomness or entropy of a macrostate with the logarithm of the number of its microstates. Supplementing this definition of randomness, we defined the order or information of a macrostate as the difference between its potential randomness or entropy (the largest value of the randomness or entropy consistent with given constraints) and the actual value. Thus maximally random macrostates have zero order and maximally ordered macrostates have zero randomness. According to these definitions, a physical system far removed from thermodynamic equilibrium (the macrostate of maximum randomness) is highly ordered. So is a protein whose biological fitness can't be improved by changes in its sequence of amino acids: it belongs to a very small subset of the class of polypeptides of the same length.

These definitions of randomness and order are important not just, or even primarily, because they lend precision to the corresponding intuitive notions in a wide range of scientific contexts. They are important primarily because they are adapted to theoretical accounts of the growth and decay of order. Boltzmann himself proved (under restrictive assumptions) that molecular interactions in a gas not already in its most highly random macrostate increase its randomness. In Chapter 8 we saw how the cosmic expansion generates chemical order (chemical abundances far removed from those that would prevail in thermodynamic equilibrium); in Chapter 9 we discussed the origin and growth of structural order in the astronomical Universe; and in Chapters 10 and 11 we saw how random genetic variation and differential reproduction generate the biological order encoded in genetic material.

Astronomical and biological order-generating processes are hierarchically linked in the manner discussed in Chapter 2. Each process requires initial conditions generated by earlier processes. For example, the first self-replicating molecules needed an environment that provided high-grade energy, molecular building
blocks, and catalysts. High-grade energy was supplied, directly or indirectly, by sunlight, produced by the burning of hydrogen deep inside the Sun. To understand why hydrogen is so abundant, we have to go back to the early Universe, when the primordial chemical composition of the cosmic medium was laid down by an interplay between nuclear reactions and the cosmic expansion. Apart from hydrogen, the atoms that make up biomolecules (carbon, oxygen, and nitrogen are the most common) were synthesized in exploding stars far more massive than the Sun. So, too, were inorganic catalysts like zinc and magnesium. Finally, the emergence of an environment favorable to life as we know it resulted from planet-building processes, for which we still lack an adequate theory.

Although some of the specific order-generating processes we have discussed are speculative or controversial, the general principles underlying the emergence of order from chaos seem more secure. In particular, we can now understand why, in spite of the second law of thermodynamics, the Universe is not running down. The Second Law states that all natural processes tend to increase randomness. In an ordinary isolated system, the growth of randomness leads inevitably to a decline of order, because the sum of randomness and order is a fixed quantity.

in the expanding universe, information can increase at the same time as entropy increases, satisfying the second law

The Universe, however, is not an ordinary isolated system. Because space is expanding, the sum of randomness and order is not a fixed quantity; it tends to increase with time. Hence a gap may open up between the actual randomness of the cosmic medium and its maximum possible randomness. This gap represents a form of order. Chemical order (as evidenced by the prevalence of hydrogen) emerges when equilibrium-maintaining chemical reactions can no longer keep pace with the cosmic expansion. Structural order (in the form of astronomical systems) emerges when the uniform state of an expanding medium becomes unstable—that is, less than maximally random.

By making randomness an objective property of the Universe, the Strong Cosmological Principle also objectifies the timebound varieties of order, which consist in the absence of randomness. The infinitely detailed world picture of Laplace's Intelligence is devoid of macroscopic order. It contains no objective counterpart to astronomical or biological order. Laplace's Intelligence is an idiot savant. It knows the position and velocity of every particle in the Universe; but because this vast fund of knowledge (or its quantal-counterpart) is complete in itself, there is no room in it for information about stars, galaxies, plants, animals, or states of mind. In this book I have argued that the external world — the world that natural science describes — is fundamentally different from the universe of Laplace and Einstein, which is given once and for all in space and time (or in spacetime). It is a world of becoming as well as being, a world in which order emerged from primordial chaos and begot new forms of order. The processes that have created and continue to create order obey universal and unchanging physical laws. Yet because they generate information, their outcomes are not implicit in their initial conditions.

Creative Processes

All order-generating processes may be said to be creative, but some seem to deserve the label more than others. For example, the evolution of chemical order in the early Universe seems less creative than the evolution of biological order. To gain insight into this difference, let's compare the evolution of a star cluster with the evolution of a biological population. Suppose we are given a statistical description of the cluster's initial state and asked to calculate its subsequent evolution. To do the calculation, we have to assign an initial position and velocity to each star. This can be done in many different ways that are consistent with the given statistical description of the initial state, and different assignments will yield different evolutionary trajectories. But if the number of stars is large, these evolutionary trajectories diverge very little, because each star responds to the combined attraction of all the others, and the combined attraction is insensitive to statistical fluctuations in the cluster's initial state.

Now consider a biological population. Suppose we knew everything that could in principle be known about the population's initial state, including the genotypes of all the organisms belonging to the population. Suppose we also had the ability to simulate on a supercomputer every relevant aspect of the evolutionary process.

Could we then predicts what genotypes would be present in the population at some later time?

No — at least not for a population undergoing significant evolutionary change. The reason is that evolutionary outcomes are very sensitive to some of the random genetic changes brought about by mutation and genetic recombination. Suppose we could enumerate all the possible outcomes of every mutational and recombinational event and assign a probability to each of them. We would then be able, in principle, to construct a complete statistical description of our evolving population. This description would encompass a vast number of qualitatively distinct, multiply branching pathways, each with only a tiny probability of being realized. It would therefore contain very little information about the history of any given population. A prediction about the outcome of a horse race that assigns small and nearly equal probabilities of winning to each of a large number of entrants isn't very informative.

Biological evolution, therefore, not only generates order and information, but does so in an essentially unpredictable way. This, I suggest, is an essential element of every truly creative process. A creative process not only generates order, but does so in an essentially unpredictable way.

We don't yet fully understand the biological basis of creative human activity, but I find the analogy with biological evolution compelling. In Chapter 14 I suggested that higher mental processes are mediated by a cyclic process in which the brain constructs, tests, and modifies internal representations. It is tempting to
speculate that the process by which internal representations are constructed has a strong random component, in addition to systematic components that are built up in the course of individual development and that constrain and channel the random component. The systematic components would play a role analogous to that of beta genes in the evolutionary theory sketched in Chapter 11. They would be responsible for the elements of an artist's work that we recognize as his or her individual style.

[Answer to question 3]: Creative human activity is unpredictable in the same way and for the same reasons that biological evolution is unpredictable. Unpredictability, however, is only one aspect of human freedom. We are free because we are, to a considerable extent, the authors of our own lives, and because every human life is something new under the Sun. That is what Democritus and Socrates believed; and if the picture I have sketched in this book is correct in its main outlines, it is also one of the lessons of modern science. Our awareness of the openness of the future and of our own ability to help shape it reflects a deep property of objective reality.

The scientific worldview sketched in the preceding pages offers an alternative to reductionism in both its physical and its biological forms. It shows us that the Universe is more than a collection of elementary particles governed by immutable mathematical laws. Order and the processes that bring order into being lie at the heart of reality. Biological evolution, cultural evolution, and individual human lives not only are the most prolific sources of order in the known Universe, but also are creative. Because of them, the future is genuinely open.

Strong Cosmological Principle

The Strong Cosmological Principle (SCP) is a speculative interpretation of quantum indeterminacy based on Einstein's idea that the probabilities of different experimental results are simply the frequencies of the different results in an "assembly" - a large number of identical experiments. In the Schrödinger's Cat thought experiment, for example, the SCP simply says that in a certain fraction of the experiments the cat is alive, in the remaining fraction, dead.

The SCP starts from Einstein's cosmological principle that the properties (and the physical laws) of the universe do not single out any particular place in the universe. Astronomical observations have confirmed that the average properties of the universe are the same everywhere in space and they are the same in all directions from any given point. The universe is statistically uniform and isotropic.

Layzer says that his interpretation of quantum theory differs from Einstein's in an important way.

Einstein believed that quantum theory applies to assemblies rather than to individual systems because individual systems are governed by as-yet undiscovered deterministic laws. I have argued that quantum theory applies to assemblies rather than to individual systems because a complete physical reality doesn't refer to individual systems but only to assemblies. The smallest fragment of the Universe we can meaningfully describe is an assembly. If the members of the assembly are in identical microstates, there is no harm in treating them as individuals. But if they are quantal systems coupled to (macroscopic) measuring devices, we run into paradoxes like those we have discussed when we assume that quantum theory applies to them directly as individuals.

Do We Exist in Multiple Copies?

Are the assemblies we have been discussing "real"? Does the Strong Cosmological Principle imply that somewhere in the Universe there is a star very much like the Sun; and orbiting that star, a planet very much like the Earth; and on that planet, a person very much like you, the reader, reading a book very much like this one? Of course, such near-replicas of the Earth and its inhabitants would be
very thinly distributed in space. Although I haven't made a serious estimate, I am
confident that the nearest one would lie well beyond the most distant galaxy we could observe, even with infinitely sensitive instruments, Even so, the idea is unsettling, however familiar it may be to readers of science fiction. Must we accept it if we accept the Strong Cosmological Principle?

I think not. The Strong Cosmological Principle doesn't prescribe the contents of the Universe; on the contrary, it drastically limits the predictive scope of physical laws. What can be known and predicted are statistical properties only. Statistical predictions, however, do not prescribe all the properties of infinite collections...The probability of an outcome is the fraction of times it occurs in an infinite set of "trials."

The Many-Worlds Interpretation of Quantum Theory

The interpretation of quantum theory discussed in this chapter resembles in some respects the "many-worlds" interpretation proposed by Hugh Everett in 1957. Everett, in a Ph.D. thesis supervised by John Wheeler, suggested that every measurement or measurement-like process causes the Universe to split into a vast number of "parallel universes," in each of which one possible outcome of the measurement is realized. In one set of universes, Schroedinger's cat lives; in another, it dies. Quantum theory, according to this interpretation, doesn't describe individual physical systems, as in the orthodox and instrumental interpretations; nor does it describe assemblies of physical systems, as in the interpretation based on the Strong Cosmological Principle. It describes a multitude of universes, each of which splits at every moment into a multitude of parallel universes. All these universes are equally real, but only the one we happen to be in is real to us; all the others are completely inaccessible to us.

According to the many-worlds interpretation, the probability that a measurement has a given outcome is equal to the fraction of the parallel universes in which that outcome occurs. Since probabilities are real numbers that can assume any value between zero and one, the set of parallel universes must be infinite. Every measurement or measurement-like process in every universe therefore creates an infinity of new parallel universes.

The many-worlds interpretation shares two attractive features of the interpretation based on the Strong Cosmological Principle. It avoids the paradoxes that result from the conventional assumption that quantum theory describes individual systems. And it predicts, instead of merely positing, the basic rule mentioned earlier for calculating the probabilities of experimental outcomes. [Probabilities are proportional to the number of outcomes in the assembly.]

If quantum physics describes assemblies of identical systems obeying the Strong Cosmological Principle, as I have proposed in this chapter, it doesn't have to be supplemented by ad hoc postulates about measurement. Formulated in this way, the theory predicts that measurements have definite but unpredictable outcomes, and that the probability of any given outcome is given by the usual rule.

In each individual system, everything is determined, but in the assembly of all systems, the Strong Cosmological Principle insures there will be a variety of objectively indeterminate outcomes.

Layzer says that the fact that we don't know which of the many possible systems we are in means that our future is indeterminate, more specifically that our current state has not been predetermined by the initial state of the universe.

Other Multiple World Ideas

In ancient times, Lucretius commented on possible worlds.
In his De Rerum Natura, he wrote in Book V,

for which of these causes holds in our world it
is difficult to say for certain ; but what may be done
and is done through the whole universe in the various
worlds made in various ways, that is what I teach,
proceeding to set forth several causes which may
account for the movements of the stars throughout
the whole universe; one of which, however, must
be that which gives force to the movement of the
signs in our world also; but which may be the true
one,

(De Rerum Natura, Book V, lines 526-533

The idea of many possible worlds was also proposed by Gottfried Leibniz, who famously argued that the actual world is "the best of all possible worlds." Leibniz says to Arnauld in a letter from 14 July 1686,

I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God which are distinctive of it, that is, certain primary free decrees (conceived sub ratione possibilitatis) or certain laws of the general order of this possible universe with which they are in accord and whose concept they determine, as they do also the concepts of all the individual substances which must enter into this same universe.

(Die philosophischen Schriften., II 51/L 333)

Leibniz' notion of a substance was so complete that it in principle could be used to deduce from it all the predicates of the subject (the "bundle" of all properties) to which this notion is attributed.

Hugh Everett III's many-worlds interpretation of quantum mechanics is an attempt to deny the random "collapse" of the wave function and preserve determinism in quantum mechanics. Everett claims that every time an experimenter makes a quantum measurement with two possible outcomes, the entire universe splits into two new universes, each with the same material content as the original, but each with a different outcome. It violates the conservation of mass/energy in the most extreme way.

The Everett theory preserves the "appearance" of possibilities as well as all the results of standard quantum mechanics. It is an "interpretation" after all. So even wave functions "appear" to collapse. Note that if there are many possibilities, whenever one becomes actual, the others disappear instantly in standard quantum physics. In Everett's theory, they become other possible worlds.

The human ignorance of not knowing which universe we are in Layzer calls a macroscopic indeterminism that does solve the free will problem. If Layzer is right, the logically possible worlds of David Lewis and the many worlds of physicist Hugh Everett also solve the free will problem.

Note that Kripkje's possible worlds are extremely close to one another. The quantification of information in each case shows a very small number of bits as the difference between them, especially when compared to the typical examples given in possible worlds cases. In the case of Humphrey winning the election, millions of persons must have done something different. Such worlds are hardly "nearby." For typical cases of a free decision, the possible worlds require only small differences in the mind of a single person.

By comparison, the possible worlds of Hugh Everett, David Lewis, and David Layzer in general may bear very little resemblance to one another. But note that they all include Layser's solution to the problem of free will, at least in those worlds with thinking beings, because the inhabitants do not know which of all the possible worlds they are in.

______, 1971, "Cosmogonic Processes," in Astrophysics and General Relativity, two volumes, edited by Max Chrétien, Stanley Deser, and Jack Goldstein, Gordon and Breach, NY. [Summer institute at Brandeis, 1968 - the first appearance of Growth of Order?]